Entanglement Without Metaphysics: An Operator-Level Analysis
How a Pre-κ Operator Reveals Hidden Nonseparability in Recursive Dynamics
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Demonstrating Utility as a Structural Law Beyond Operator Control
From Operator Control to Structural Laws: The Complete Axis II→III Research Arc
Abstract
This article presents the culmination of a systematic research program spanning four experimental chambers (XLIV–XLVII) and two complete research axes. Through pre-registered experiments with decisive falsification criteria, we establish that worldline-local utility is not controllable through operator-level mechanisms (Axis II falsified) but is instead a structural admissibility property of grammar–topology classes (Axis III confirmed). We demonstrate that utility emerges only in structures with irreversible convergence of independent histories—specifically, directed acyclic graphs (DAGs)—while remaining inadmissible in tree-based structures. This finding elevates a previously empirical observation (worldline commitment) to a structural theorem with precise mathematical conditions.
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Utility Lives Where Return Is Impossible
How Irreversible Generative Asymmetry Unlocks Compositional Utility in Physics-Like Systems
Abstract
For three chambers across Axis I (XLI–XLIII), UNNS demonstrated a structural closure result: within symmetric, locally editable recursive grammars, compositional utility does not emerge, even under state collapse, parameter mutation, and selection pressure. Every mechanism that operated on grammars after generation failed categorically.
Chamber XLIV introduces a single new primitive: irreversible branching during generation. The result is the first validated breach of grammar closure. Utility emerges—but not as a property of laws, parameters, or ensemble averages. It emerges as a property of specific, irreversibly committed worldlines.
This result reframes fundamental questions in physics: from "why these laws?" to "which histories are allowed to exist?" The implications extend to quantum foundations, cosmology, and the emergence of structure in any physics-like system.
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When the Substrate
Says No
Empirical evidence for structural limits in symmetric recursive grammars
What We Discovered
Across three validated selection chambers, we have established that compositional utility is categorically forbidden within symmetric, locally editable recursive grammars—even under persistent selection pressure and active grammar manipulation.
This is not a failure to find utility. This is a structural discovery: within the {τ,σ,κ,ρ} operator algebra, permission for utility is not negotiated at the compositional adjacency layer. The substrate exhibits sharp boundaries where structures either project stably with zero utility, or fail to project entirely.
We distinguish two types of negatives: diagnostic (mechanism refuses to engage) and systematic (mechanism works, substrate indifferent). Together, these establish that utility constraints operate independent of and prior to grammar manipulation attempts.